Rates and architectures for learning geometrically non-trivial operators

arXiv — cs.LGThursday, December 11, 2025 at 5:00:00 AM
  • A recent study has expanded the learning theory in deep learning by demonstrating that double fibration transforms, which include generalized Radon and geodesic ray transforms, can be effectively learned from limited data. This advancement addresses the challenges of recovering operators in high-dimensional spaces, particularly those involving singularities, which are common in mathematical physics and fluid dynamics.
  • This development is significant as it enhances the capabilities of scientific machine learning, allowing for more efficient operator recovery in complex scenarios. The ability to learn these geometrically non-trivial operators without succumbing to the curse of dimensionality could lead to breakthroughs in various applications, including wave propagation and fluid dynamics.
  • The integration of advanced learning techniques in operator recovery reflects a broader trend in artificial intelligence, where data efficiency and the ability to handle complex geometries are increasingly prioritized. This aligns with ongoing research in machine learning that seeks to improve performance in diverse fields, from robotic perception to digital signal processing, highlighting the interconnectedness of these advancements.
— via World Pulse Now AI Editorial System

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